Question

A wooden piece can float both in mercury (of density $ 13.6\,g/cc $ ) and in water (of density $ 1\,gm/cc $ ). The ratio of mass of mercury displaced to the mass of water displaced is

• A. $ 1 $
• B. $ 13.6 $
• C. $ \frac{1}{13.6} $
• D. $ \frac{12.6}{13.6} $

Answer 1

Answer: (A)

If the same body is made to float in different liquids of density $\sigma_{A}$ and $\sigma_{B}$ respectively.
$V_{P}=\left(V_{m}\right)_{A} \sigma_{A}=\left(V_{m}\right)_{B} \sigma_{B}$
$\therefore \frac{m_{A}}{m_{B}}=1$